Electron. J. Diff. Equ., Vol. 2011 (2011), No. 63, pp. 1-12.

Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters

Stefan Liebscher

We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant foliation at the singularity transverse to the manifold of equilibria. We call this setting bifurcation without parameters. We provide a description of general systems with a manifold of equilibria of codimension one as a first step towards a classification of bifurcations without parameters. This is done by relating the problem to singularity theory of maps.

Submitted April 10, 2010. Published May 17, 2011.
Math Subject Classifications: 34C23, 34C20, 58K05.
Key Words: Manifolds of equilibria; bifurcation without parameters; singularities of vector fields.

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Stefan Liebscher
Free University Berlin, Institute of Mathematics
Arnimallee 3, D-14195 Berlin, Germany
email: stefan.liebscher@fu-berlin.de

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